For the Pimento Cheese, mix together the cheddar, pimentos, mayonnaise, vinegar, garlic powder and cayenne pepper and refrigerate for half an hour before using.
For the Sandwich, cook bacon in skillet over medium heat until crisp. Remove and drain on paper towels. Place two slices of rye bread on a plate. Spread desired amount of pimento cheese onto one slice. Top with cooked bacon and sliced avocado, evenly.
Place the second slice on top. Spread even layer of butter on top of the bread. Slip over the sandwich and do the same to the other side.
Heat a skillet over low heat. Once heated, place sandwich on skillet. Heat over low heat for a few minutes, checking occasionally to make sure it doesn’t get too brown.
Flip the sandwich over. Lightly press on the sandwich with a spatula. Let it cook for another few minutes, until the cheese is somewhat melted, and the bread is golden brown.